Seismic data acquisition and processing techniques are used to generate a profile (image) of a geophysical structure (subsurface) of the strata underlying the land surface or seafloor. Among other things, seismic data acquisition involves the generation of acoustic waves and the collection of reflected/refracted versions of those acoustic waves to generate the image. This image does not necessarily provide an accurate location for oil and gas reservoirs, but it may suggest, to those trained in the field, the presence or absence of oil and/or gas reservoirs. Thus, providing an improved image of the subsurface in a shorter period of time is an ongoing process in the field of seismic surveying.
Considering the characteristics of ocean-bottom-node (OBN) data processing, pressure data (P), recorded by hydrophones and vertical particle velocity data (Vz), recorded by geophones are jointly processed for the separation of upward traveling and downward traveling wave fields. Based on the fact that upward traveling waves in P data and Vz data have the same polarity and downward traveling waves in P data and Vz data have opposite polarity, as shown in the equations:P=U+D and Vz=(kz/ρω)(U−D)  (1)and described by B. H. Hoffe, L. R. Lines and P. W. Cary in their 2000 article entitled “Applications of OBC Recording: The Leading Edge,” published in The Leading Edge, 19, page 382 and incorporated herein by reference, the summation of the P data and the Vz data can separate the upward traveling waves from the downward traveling waves.
A complicating factor associated with the above described wavefield separation derives from the fact that the Vz data usually contains shear wave noise that does not exist in the P component of the wave data, as described by J. Paffenholz, P. Docherty, R. Shurtleff and D. Hays in their 2006 article entitled “Shear Wave Noise on OBS Vz Data—Part II Elastic Modeling of Scatterers in the Seabed,” published in EAGE 68th Conference and Exhibition, B047 and incorporated herein by reference. Accordingly, the shear wave noise in the Vz component needs attenuated before the Vz wavelets and the P wavelets can be matched and summed.
Continuing with the wavefield separation, shear wave noise attenuation in Vz and matching between P and Vz can be achieved in one step with local attribute matching in a dual-tree complex wavelet transform (DTCWT) domain as described by Z. Yu, C. Kumar and I. Ahmed (hereinafter YU) in their 2011 article entitled “Ocean Bottom Seismic Noise Attenuation Using Local Attribute Matching Filter,” published in SEG Technical Program, Expanded Abstracts, 30, pages 3586-3590 and incorporated herein by reference. A two-dimensional (2D) DTCWT is applied to both the P components and the Vz components to obtain two sets of complex coefficients as described by I. W. Selesnick, R. G. Baraniuk and N. G. Kingsbury (hereinafter SELESNICK) in their 2005 article entitled “The Dual-Tree Complex Wavelet Transform,” published in IEEE Signal Processing Magazine, 22, pages 123-151 and incorporated herein by reference. The amplitude of each complex coefficient of a Vz wavelet is matched to the amplitude of a corresponding P wavelet while preserving the phase of the wavelets, leading to a suppression of the shear noise in the Vz data.
Looking to how 2D DTCWT is implemented in a row-column separable way, as described by SELESNICK, i.e., analyzing filters are applied in rows and columns separately in analysis stages, wherein each analysis stage is equivalent to dividing the input F-K domain into the four sub-bands of HH band (high-f, high-k), HL band (high-f, low-k), LH band (low-f, high-k) and LL band (low-f, low-k). Continuing, the next analysis stage is recursively performed only within the LL band. Accordingly, in conventional 2D DTCWT the division of the input F-K domain is similar to FIG. 3(a) and this division pattern has an intrinsic problem, i.e., high-k components have poor frequency resolution in the low frequencies.
Evaluating field seismic data indicates that shear wave noise in Vz usually exists in a large k range and in a low frequency range. Unfortunately, with the conventional 2D DTCWT band division, high-k shear noise cannot be adequately isolated in the frequency domain and therefore attenuation of high-k shear noise is inhibited. In another aspect, the drawbacks associated with the conventional 2D DTCWT are caused by the limit of angle resolving capability. In conventional 2D DTCWT, every stage has three wavelet bands, i.e, the LH band, the HH band and the HL band, and each band accommodates two 2D wavelet bases that are conjugate to each other. According to SELESNICK and YU, every stage accommodates exactly six orientations of the 2D wavelets. However, the limitation of six orientations restricts the angular resolving capability of the conventional 2D DTCWT, i.e., for high-f or high-k bands in the early analysis stages, the wavelet bases are sharp and should have a detailed angular resolving capability to resolve more than six orientations.
Accordingly, it would be desirable to provide systems and methods that avoid the afore-described problems and drawbacks.